A note on adiabatic time evolution and quasi-static processes in translation-invariant quantum systems

TL;DR

This paper investigates the behavior of translation-invariant quantum systems undergoing slow, quasi-static evolution, revealing structural properties and showing incompatibility with certain equilibrium approaches.

Contribution

It combines the Gibbs variational principle with quantum weak Gibbs states to analyze quasi-static processes in translation-invariant quantum systems.

Findings

Quasi-static processes are incompatible with approach to equilibrium.

Structural results on quantum weak Gibbs states.

Analysis applies to spin and fermion systems on lattices.

Abstract

We study the slowly varying, non-autonomous quantum dynamics of a translation invariant spin or fermion system on the lattice $\mathbb Z^d$. This system is assumed to be initially in thermal equilibrium, and we consider realizations of quasi-static processes in the adiabatic limit. By combining the Gibbs variational principle with the notion of quantum weak Gibbs states introduced in [Jak\v{s}i\'c, Pillet, Tauber, arXiv:2204.00440], we establish a number of general structural results regarding such realizations. In particular, we show that such a quasi-static process is incompatible with the property of approach to equilibrium studied in this previous work.